Rare decays of \(B\)  mesons are sensitive probes to study possible new physics beyond the Standard Model (SM). In the SM, the decay \(B^0 \rightarrow c\bar{c} \gamma \)  proceeds dominantly through an exchange of a \(W\)  boson and the radiation of a photon from the \(d\)  quark of the \(B\)  meson (Fig. REF ). Many theoretical predictions of branching fractions depend on the factorization approach of QCD interactions in the decay dynamics. In the case of \(B^0 \rightarrow J/\psi \gamma \) , the branching fraction has been predicted to be \(7.65 \times 10^{-9}\)  using QCD factorization [1]} and \(4.5 \times 10^{-7}\)  when using a perturbative QCD (pQCD) approach [2]}.
Possible new physics enhancements of the branching fractions may be due to right-handed currents [1]} or nonspectator intrinsic charm in the \(B^0\)  meson [4]}. Currently, the upper limit for \(B^0 \rightarrow J/\psi \gamma \)  is \(1.5 \times 10^{-6}\)  at 90% confidence level [5]}.
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